Dipole graph
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In graph theory, a dipole graph, dipole, bond graph, or linkage, is a multigraph consisting of two vertices connected with a number of parallel edges. A dipole graph containing Template:Mvar edges is called the size-Template:Mvar dipole graph, and is denoted by DnScript error: No such module "Check for unknown parameters".. The size-Template:Mvar dipole graph is dual to the cycle graph CnScript error: No such module "Check for unknown parameters"..
The honeycomb as an abstract graph is the maximal abelian covering graph of the dipole graph D3Script error: No such module "Check for unknown parameters"., while the diamond crystal as an abstract graph is the maximal abelian covering graph of D4Script error: No such module "Check for unknown parameters"..
Similarly to the Platonic graphs, the dipole graphs form the skeletons of the hosohedra. Their duals, the cycle graphs, form the skeletons of the dihedra.
References
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- Jonathan L. Gross and Jay Yellen, 2006. Graph Theory and Its Applications, 2nd Ed., p. 17. Chapman & Hall/CRC. Template:ISBN
- Sunada T., Topological Crystallography, With a View Towards Discrete Geometric Analysis, Springer, 2013, Template:ISBN (Print) 978-4-431-54177-6 (Online)